If someone else is paying I'd recommend this place ( [broken link removed] ) - very cool altogether, lovely large rooms very nicely decorated, fabulous breakfast too, but pricey.
I'm sure you can get very decent accommodation for a lot less than that but I've no recommendations ... The best site for hotel reservations in my opinion is www.hrs.com .. they are a german company so should have loads of hotels listed for Hamburg.
The Ibis hotel is a good choice if you want cheap and basic. Rooms are like prison cells but the food/drink is ok. No facilities as such and the bedroom carpet is so thin you can 'feel' the concrete underneath!!
It's close to the entertainment area (which also doubles as a tolerated 'red-light area'). Locals don't bat an eyelid but it was be a bit 'odd' the first time I (male) walked through the area. And me a bleddin' Nortsider!